Improved complexity bounds for second-order convex finite-sum optimization
Original title: Near-Optimal Second-Order Convex Finite-Sum Optimization under Individual Smoothness
The paper matches a new lower bound of Omega(n + n^{5/7} eps^{-2/7}) using a Taylor-corrected lazy Newton method with Monteiro-Svaiter acceleration.
Stochastic second-order oracle complexity is studied for smooth convex finite-sum optimization. Individual smoothness enables further acceleration beyond averaged assumptions. A new self-bounding inequality leads to the matching upper bound.
From the original article
1 min read at arxiv.orgWe study the stochastic second-order oracle complexity of solving smooth convex finite-sum optimization with $n$ components. Very recently, Tsedenov \& Kovalev (2026) showed that the minimax optimal complexity under averaged smoothness and convexity is $\tildeΘ(n + n^{6/7} ε^{-2/7})$ by establishing nearly matching upper and lower bounds.
By Xinliang Zhang · arxiv.org
A short excerpt; the article and its images belong to the publisher. Summary, key facts and assessment above are AI-written from the article and can be wrong.